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This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve prediction-correction steps to provably track the trajectory of the optimal solutions of time-varying convex problems. The merits of existing prediction-correction methods...
We consider non-differentiable convex optimization problems that vary continuously in time and we propose algorithms that sample these problems at specific time instances and generate a sequence of converging near-optimal decision variables. This sequence converges up to a bounded error to the solution trajectory of the time-varying non-differentiable problems. We illustrate through analytical examples...
Constrained optimization problems that couple different cooperating users sharing the same communication network are often referred to as multiuser optimization programs. We are interested in convex discrete-time time-varying multiuser optimization, where the problem to be solved changes at each time step. We study a distributed algorithm to generate a sequence of approximate optimizers of these problems...
We consider a robotic network composed of mobile robots capable of communicating with each other. We study the problem of collectively tracking a number of moving targets while maintaining a certain level of connectivity among the robots, by moving them into appropriate positions. The distances of the robots to each other and to the targets are used to define a communication and target tracking graph,...
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